Answer

$\cos^2\theta(\tan^2\theta+1)=1$

Work Step by Step

Start with the left side:
$\cos^2\theta(\tan^2\theta+1)$
Use the identity $\tan^2\theta+1=\sec^2\theta$:
$=\cos^2\theta\sec^2\theta$
$=\cos^2\theta*\frac{1}{\cos^2\theta}$
$=1$
Since this equals the right side, the identity has been proven.